It is known in the art to use steel plates as a material for the clutch drums of the high-and-reverse and forward drive clutches for achieving reduction of cost. The thickness of the plate for the clutch drums is determined corresponding to the external force applied to such drums under operation of the transmission. Usually, the clutch drum for the high-and-reverse clutch is constructed of relatively thick steel plate in comparison with that for the forward drive clutch since the clutch drum of the high-and-reverse clutch should tolerate not only the force applied thereto by a brake band wrapping the same but also the force generated by pressurized fluid in a piston chamber defined therein. However, from the mechanical point of view, it is usual to design and construct the high-and-reverse clutch such that the clutch plates thereof are splined to grooves formed on a separate cylindrical member of steel plate which is coaxially held in the clutch drum, while the forward drive clutch is such designed that the clutch plates thereof are splined to openings formed in the clutch drum thereof. The grooves of the separate cylindrical member of the high-and-reverse clutch are formed by press forming so that each groove is shaped to have a trapezoidal cross section (see FIG. 3) by the nature of the press forming technique. This induces a necessity of shaping detents or teeth of the clutch plates into a trapezoidal form for achieving effective spline connection between the clutch plates and the cylindrical member of the high-and-reverse clutch. On the other hand, the openings of the clutch drum of the forward drive clutch are formed by punching, so that two facing shared surfaces of each opening are left paralleled, inevitably. As is known in the art, effective spline connection is not expected from the engagement between the trapezoidal teeth and the opening having such parallelly shared surfaces. Thus, the high-and-reverse clutch and the forward drive clutch of the type mentioned above cannot use common clutch plates, inducing difficulty in increasing productivity of the clutches and thus difficulty in reducing cost of the transmission.